If your cutesy-ometer is exquisitely sensitive, stay away from “King & Maxwell,” TNT’s new private eye series. It will send your little arrow into the red, your eyes will roll toward the skies, and your cynicism alarm will sound, loudly.

The show, which premieres Monday night at 10, is filled with cutesy, flirty banter between two former Secret Service agents who work together as P.I.s. He is the charming, handsome, and wily Sean King, played by Jon Tenney; she is the fearless and beautiful Michelle Maxwell, played by Rebecca Romijn. They spend a lot of time being coy with each other while tripping up and catching bad guys in the D.C. area; we spend a lot of time asking that most timeworn of TV questions: “Will they or won’t they?”

“King & Maxwell” is based on a book series about the pair by David Baldacci, but it is also a descendant of romantic-tension TV procedurals such as “Remington Steele” and “Moonlighting.” The sexual overtones and repartee between Sean and Michelle — and not the crimes of the week — are the point of the series. And there does seem to be some potential for chemistry between Romijn and Tenney, seen elsewhere on TNT on “The Closer” and its spinoff, “Major Crimes.” They are likable enough together and game for good-humored repartee. But ultimately they can’t lift the show above the middling material. Sean and Michelle work in a picturesque little boathouse office on a river, and after she rows there in the mornings, she strips down in the bathroom to shower so that he can almost-almost-almost see. She leaves the door open because, she says, she doesn’t like the steam; he ogles. When it’s not creepy, it’s pretty stale.

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The connection between Sean and Michelle is meant to be offbeat. He has some stereotypically feminine qualities, such as reading romance novels and not liking sloppiness. And she is more stereotypically male — athletic and gung-ho when it comes to fighting and guns. But it’s a bland, cliched kind of offbeat, as she teases him and he teases her in an all too familiar manner.

The sleuthing and the mild action sequences, at least based on the first episode, are hackneyed, too. If your cutesy-ometer doesn’t go bonkers, your flimsy-ometer probably will. The crimes are lazily written procedural plots, which Sean and Michelle solve without having to play by the rules. Their unconventional and sometimes illegal tricks provoke the FBI, and one agent, Frank Rigby (Michael O’Keefe), is constantly threatening them. He’s the cloud in their coffee, all humorless scowling as he accuses them of being “washed up” amateurs at every turn. While they jaunt merrily around the city, his own cutesy-ometer is clearly in constant distress.